# Pseudo-class regression for LGCA with multiply imputed data

I have fit a latent class growth analysis model (LGCA) using the lcmm package in R. I want to estimate a regression looking at predictors of class membership. I have missing data in my predictor variables.

I don't want to use the 1-step approach, because this changes the latent classes, and in any case, I have missing data. I don't want to use most likely latent class as my entropy value is only ~ 0.8, so estimates will be attenuated.

As far as I can see, I have two (potentially) viable options, but I am not sure if either of these would be valid.

Option 1

1. Run the LGCA without covariates.
2. Take m pseudo-class draws from the posterior class probabilities.
3. For each draw m, produce an imputed dataset (e.g. in mice).
4. For each m, estimate a multinomial model regressing (pseudo-)class membership on (imputed) predictor variables.
5. Combine the m estimates using Rubin's Rules.

One potential problem I see with this is that Petersen et al. (2012) provide a different formula for pooling estimates from pseudo-draws and they don't use imputed predictor data.

Option 2

1. Produce the LGCA in lcmm.
2. For each individual, extract the most likely class membership and class probabilities. Also extract the k x k table of logits for classification probabilities.
3. Produce m imputed datasets using class probabilities as auxiliary variables in the imputation model.
4. Run the third step of the manual 3-step approach in Mplus (Asparouhov and Muthen, 2014) with the imputed datasets and accounting for class membership uncertainty.

One potential problem here could be that lcmm and Mplus use different optimisers so using the former results in the latter might create a error (?).

Question

So my question is: what is the best approach? Is there another option that is better?

It would be great to here people's thoughts!

(In case it's important, I am using lcmm to estimate the model because (a) I have a preference for open-source software and (b) I am using date splines with an ordinal dependent variable, which Mplus doesn't seem to be able to handle well.)

Thanks,

Liam